The answer is 9.67 hours...but not sure how to get there

As this facility is starting up the reactor (which is initially empty but can hold 1500 kg) needs to be filled with the feed. The reactor is initially filled slowly at a rate of 10 kg/h but the rate starts to immediately increase linearly until the reactor is full. After three hours, the filling rate is 10- fold the initial rate. How long will it take to fill the reactor completely (hr)? CONDENSER Off-gas to scrubber CONDENSER Distillate 99 mole% CHCHO1) Condensate 45 mole% CH3OH(1) Feed: C2H,OH(1) DISTILLATION COLUMN REACTOR 55 mole% CH2CHO(1) Reactor output: H, C2H,OH(v), CHCHO(v) Recycle 95 mole% CHOH(1) 5 mole% CHCHO) REBOILER